The town is located at the southern edge of the White Mountain National Forest.

Taking its name from Robert Marsham, 2nd Baron Romney (pronounced Rumney), the town was originally granted in 1761 by Governor Benning Wentworth to settlers from Colchester and East Haddam, Connecticut. It was first settled in 1765. Because some grantees failed to comply with the charter, Rumney was regranted to another group of settlers in 1767.

According to the US census, the town has a total area of 42.6 square miles, of which 41.7 square miles is land and 0.9 square miles is water, comprising 2.15% of the town.

As of the 2010 census, there were 1,480 people residing in the town, and according to the 2000 census there were 569 households, and 393 families residing in the town. The population density was 35.3 people per square mile. There were 879 housing units at an average density of 21.0 per square mile.

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